Angle Sum Property of Quadrilateral


 
 
Concept Explanation
 

Angle Sum Property of Quadrilateral

The word quad means four and the word lateral means sides. Thus, a plane figure bounded by four line segments AB, BC, CD and DA is called a quadrilateral and is written as quad. ABCD or, large square ABCD. The points A, B, C, D are called its vertices. The four line segments, AB, BC, CD and DA are the four sides, and the four angles large angle A, large angle B, large angle C and large angle D are the four angles of quad. ABCD, Two line segments AC and BD are called the diagonals of quad. ABCD.

Theorem : The sum of the four angles of a quadrilateral is 360.

GIVEN Quadrilateral ABCD

To Prove <A + <B + <C + <D = 360

Construction  Join BD

Proof:  In large Delta ABD, we have

      <1 + <2 + <3 = 180                .....(i)

In large Delta BCD, we have

      <4 + <5 + <6 = 180              .......(ii)

Adding (i) and (ii), we get

     <1 + <2 + <3 + <4 + <5 + <6 = 180 + 180

     <1 + (<2 + <6 )+ <5+ (<3 + <4) = 180 + 180

large Rightarrow  <A + <B + <C + <D = 360

large Rightarrow  <A + <B + <C + <D = 360

 

Illustration: In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2: 3 : 4. Find the measure of each angles of the quadrilateral.

Solution:  We have,  <A : <B : <C : <D = 1 : 2 : 3 : 4.  So, let <A = x, <B = 2x, <C = 3x, < D = 4x.

large therefore     <A + <B + <C + <D = 360

large Rightarrow      x + 2x + 3x + 4x = 360 large Rightarrow 10x = 360 large Rightarrow x = 36

Thus, the angles are

angle A=36^0

angle B=2times36^0= 72^0

angle C= 3times36^0= 108^0

angle D=4times36^0= 144^0

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Which of the following is a formula to find the sum of interior angles of a quadrilaters of n-sides?

Right Option : D
View Explanation
Explanation
Question : 2

The angles of a quadrilateral are in the ratio 3 : 5 : 7 : 9. The measure of all angles are :

Right Option : D
View Explanation
Explanation
Question : 3

Find the value of x when other three angles are : 45, 60, 150 .

Right Option : B
View Explanation
Explanation
 
Video Link - Have a look !!!
 
Language - English
 
 
 
 


Students / Parents Reviews [10]